Solution:
The total average kinetic energy \( E \) of translatory motion for an ideal gas is given by:
\[
E = \frac{3}{2} nRT
\]
where:
- \( n \) is the number of moles,
- \( R \) is the gas constant (\( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the temperature in Kelvin.
We can rearrange to find \( nRT \):
\[
nRT = \frac{2}{3} E
\]
The ideal gas law also gives us:
\[
PV = nRT
\]
Thus,
\[
P = \frac{nRT}{V} = \frac{\frac{2}{3} E}{V}
\]
Substitute \( E = 1.5 \times 10^5 \, \text{J} \) and \( V = 20 \, \text{litres} = 20 \times 10^{-3} \, \text{m}^3 \):
\[
P = \frac{\frac{2}{3} \times 1.5 \times 10^5}{20 \times 10^{-3}}
\]
\[
P = \frac{10^5}{20 \times 10^{-3}} = 5 \times 10^6 \, \text{N/m}^2
\]
So, the pressure is \( 5 \times 10^6 \, \text{N/m}^2 \).
Leave a Reply